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Simplifying 2y4 + -46y2 + 180 = 0 Reorder the terms: 180 + -46y2 + 2y4 = 0 Solving 180 + -46y2 + 2y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(90 + -23y2 + y4) = 0 Factor a trinomial. 2((5 + -1y2)(18 + -1y2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -1y2)' equal to zero and attempt to solve: Simplifying 5 + -1y2 = 0 Solving 5 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1y2 = 0 + -5 -1y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1y2 = -5 Divide each side by '-1'. y2 = 5 Simplifying y2 = 5 Take the square root of each side: y = {-2.236067978, 2.236067978}Subproblem 2
Set the factor '(18 + -1y2)' equal to zero and attempt to solve: Simplifying 18 + -1y2 = 0 Solving 18 + -1y2 = 0 Move all terms containing y to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1y2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1y2 = 0 + -18 -1y2 = 0 + -18 Combine like terms: 0 + -18 = -18 -1y2 = -18 Divide each side by '-1'. y2 = 18 Simplifying y2 = 18 Take the square root of each side: y = {-4.242640687, 4.242640687}Solution
y = {-2.236067978, 2.236067978, -4.242640687, 4.242640687}
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